"저는 스물아홉 살입니다."
Translation:I am twenty-nine years old.
No. The native Korean counting system is used for counting things, including age with 살.
Although, you would use the sino-Korean counting (such as 이십구) if you use your age with 세. And I believe with "세", you'd use your international age rather than the traditional Korean age.
By the way, I've now seen that I was slightly incorrect.
The difference is that you use 세 to describe someone who is your elder or someone you're trying to show respect to. But otherwise they're the same and use regular Korean age.
So, like on the news if they have a 50 year old guy, they'll write about him as "오십세" or "50세", but he'd describe himself using "쉰살".